point set

In mathematics, a point set is a collection of points, often within geometry or topology. This concept is fundamental to point set topology, a branch of topology that studies topological and metric spaces using set theory.12

A topological space is a generalization of Euclidean spaces where closeness is defined by relationships between sets rather than distance. It comprises a set of points and a class of open subsets that follow specific rules for unions and intersections. The idea of a limit point is crucial: a point is a limit point of a set if every open set containing it also contains other points from that set.3

Set theory, developed by Georg Cantor, is a branch of mathematics that examines well-defined collections of objects, known as sets. It provides a precise language for complex mathematical concepts and revolutionized mathematics by treating infinite sets as valid mathematical objects.4